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Question 0121
Equations and Inequalities
2021 Paper 1 Question 1 Variant
Question
Generate new
A function
f
{f}
f
is defined by
f
(
x
)
=
a
x
3
+
b
x
2
+
c
x
+
d
.
{f(x)=ax^3+bx^2+cx+d.}
f
(
x
)
=
a
x
3
+
b
x
2
+
c
x
+
d
.
The graph of
y
=
f
(
x
)
{y=f(x)}
y
=
f
(
x
)
passes through the points
(
1
,
14
)
{(1, 14)}
(
1
,
14
)
and
(
−
1
,
−
14
)
.
{(-1, - 14).}
(
−
1
,
−
14
)
.
The graph has a turning point at
x
=
1
,
{x=1,}
x
=
1
,
and
∫
0
1
f
(
x
)
d
x
=
10.
{\displaystyle \int_0^1 f(x) \; \mathrm{d}x = 10.}
∫
0
1
f
(
x
)
d
x
=
10.
Find the values of
a
,
b
,
c
{a,b,c}
a
,
b
,
c
and
d
.
{d.}
d
.
[5]
Answer
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